Question

which function is equivalent to $f(x) = 2(x - 4)^2 + 3$?
a $f(x) = 2x^2 - 16x - 29$
b $f(x) = 2x^2 - 29$
c $f(x) = 2x^2 - 16x + 35$
d $f(x) = 2x^2 + 35$

Explanation:

Step1: Expand \((x - 4)^2\)

Using the formula \((a - b)^2 = a^2 - 2ab + b^2\), where \(a = x\) and \(b = 4\), we get \((x - 4)^2 = x^2 - 8x + 16\).

Step2: Multiply by 2

Multiply the expanded form by 2: \(2(x^2 - 8x + 16) = 2x^2 - 16x + 32\).

Step3: Add 3

Add 3 to the result: \(2x^2 - 16x + 32 + 3 = 2x^2 - 16x + 35\).

Answer:

C. \(f(x) = 2x^2 - 16x + 35\)